Over Lesson 4–1 BELLRINGER: 1) Classify ΔRST . 2) Find y if ΔRST is an isosceles triangle with RS RT.
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Over Lesson 4–1
BELLRINGER:
1) Classify ΔRST .
2) Find y if ΔRST is an isosceles triangle with RS RT.
Use the Triangle Angle-Sum Theorem
SOFTBALL The diagram shows the path of the softball in a drill developed by four players. Find the measure of each numbered angle.
Understand Examine the information in the diagram. You know the measures of two angles of one triangle and only one measure of another. You also know that 1 and 2 are vertical angles.
Use the Triangle Angle-Sum Theorem
Triangle Angle-Sum Theorem
Simplify.
Subtract 117 from each side.
Plan Find m1 first because the measure of two angles of the triangle are known. Use the Vertical Angles Theorem to find m2. Then you will have enough information to find the measure of 3.
Solve
Use the Triangle Angle-Sum Theorem
Triangle Angle-Sum Theorem
Simplify.
Subtract 142 from each side.
1 and 2 are congruent vertical angles. So, m2 = 63.
Answer: Therefore, m1 = 63, m2 = 63, and m3 = 38.
Check The sums of the measures of the angles in each triangle should be 180.
m1 + 43 + 74 = 63 + 43 + 74 or 180m2 + m3 + 79= 63 + 38 + 79 or 180
A. 95
B. 75
C. 57
D. 85
Find the measure of 3.
Use the Exterior Angle Theorem
GARDENING Find the measure of FLW in the fenced flower garden shown.
mLOW + mOWL = mFLW Exterior Angle Theorem
x + 32 = 2x – 48 Substitution
32 = x – 48 Subtract x from each side.
80 = x Add 48 to each side.
Answer: So, mFLW = 2(80) – 48 or 112.
A. 30
B. 40
C. 50
D. 130
The piece of quilt fabric is in the shape of a right triangle. Find the measure of ACD.
Find Angle Measures in Right Triangles
Find the measure of each numbered angle.
If 2 s form a linear pair, they are supplementary.
Exterior Angle Theoremm1 = 48 + 56
Simplify.= 104
Substitution104 + m2 = 180
Subtract 104 from each side.76
Find Angle Measures in Right Triangles
Subtract 132 from each side.
48
Simplify.132 + m4 = 180
Substitution56 + 76 + m 4 = 180
Triangle Angle-Sum Theorem
(90 – 34) + m2 + m 4 = 180
Simplify.= 42
If 2 s form a right angle, they are complementary.
m 3 = 90 – 48
Find Angle Measures in Right Triangles
Subtract 131 from each side.49
Simplify.m5 + 143 = 180
Triangle Angle-Sum Theoremm5 + 41 + 90 = 180
m1 = 104, m2 = 76, m3 = 42, m4 = 48, m5 = 49
A. 50
B. 45
C. 85
D. 130
Find m3.
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